We consider a differential system based on the coupling of the Navier-Stokes and Darcy equations for modeling the interaction between surface and porousmedia flows. We formulate the problem as an interface equation, we analyze the associated (nonlinear) Steklov-Poincaré operators, and we prove its wellposedness. We propose and analyze iterative methods to solve a conforming finite element appro...

N.N. Bogolubov (jr.)1,2∗, Ya.A. Prykarpatsky3,4†, A.A. Ghazaryan5 1 Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russian Federation 2 Abdus Salam International Centre for Theoretical Physics, Trieste, Italy 3 Institute of Mathematics, Pedagogical University of Cracow, Poland 4 Drohobych Ivan Franko State Pedagogical University, Lviv region, Ukraine 5 The Lomonosov ...

We study the isotropic elastic wave equation in a bounded domain with boundary. We show that local knowledge of the Dirichlet-to-Neumann map determines uniquely the speed of the p-wave locally if there is a strictly convex foliation with respect to it, and similarly for the s-wave speed.

We analyze the decomposition of the enveloping algebra of the conformal algebra in arbitrary dimension with respect to the mass-squared operator. It emerges that the subalgebra that commutes with the mass-squared is generated by its Poincaré subalgebra together with a vector operator. The special cases of the conformal algebras of two and three dimensions are described in detail, including the ...

In this paper, we prove in two dimensions global identifiability of the viscosity in an incompressible fluid by making boundary measurements. The main contribution of this work is to use more natural boundary measurements, the Cauchy forces, than the Dirichlet-to-Neumann map previously considered in [7] to prove the uniqueness of the viscosity for the Stokes equations and for the Navier-Stokes ...